--------------------------------------- The Generalized Capsules for the coefficient of q^(m*n+1) mod m for the unique formal power series satisying thefunctional equation m q f(q ) f(q) = 1 + ------- 1 - q for m from 2 to 10, are as follows m is, 2 1 [- ------, [0, 1], [1, 0]] -1 + q m is, 3 1 [- ------, [0, 1, 2], [1, 2, 0]] -1 + q m is, 4 1 [- ------, [0, 1, 2, 3], [1, 2, 3, 0]] -1 + q m is, 5 1 [- ------, [0, 1, 2, 3, 4], [1, 2, 3, 4, 0]] -1 + q m is, 6 1 [- ------, [0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0]] -1 + q m is, 7 1 [- ------, [0, 1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6, 0]] -1 + q m is, 8 1 [- ------, [0, 1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7, 0]] -1 + q m is, 9 1 [- ------, [0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 8, 0]] -1 + q m is, 10 1 [- ------, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]] -1 + q This took, 0.059, seconds.